Average Error: 10.2 → 0.3
Time: 4.3s
Precision: 64
\[x + \frac{\left(y - z\right) \cdot t}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} = -\infty \lor \neg \left(\frac{\left(y - z\right) \cdot t}{a - z} \le 1.2683856510205498 \cdot 10^{298}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t} - \frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \end{array}\]
x + \frac{\left(y - z\right) \cdot t}{a - z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} = -\infty \lor \neg \left(\frac{\left(y - z\right) \cdot t}{a - z} \le 1.2683856510205498 \cdot 10^{298}\right):\\
\;\;\;\;x + \frac{y - z}{\frac{a}{t} - \frac{z}{t}}\\

\mathbf{else}:\\
\;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r500725 = x;
        double r500726 = y;
        double r500727 = z;
        double r500728 = r500726 - r500727;
        double r500729 = t;
        double r500730 = r500728 * r500729;
        double r500731 = a;
        double r500732 = r500731 - r500727;
        double r500733 = r500730 / r500732;
        double r500734 = r500725 + r500733;
        return r500734;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r500735 = y;
        double r500736 = z;
        double r500737 = r500735 - r500736;
        double r500738 = t;
        double r500739 = r500737 * r500738;
        double r500740 = a;
        double r500741 = r500740 - r500736;
        double r500742 = r500739 / r500741;
        double r500743 = -inf.0;
        bool r500744 = r500742 <= r500743;
        double r500745 = 1.2683856510205498e+298;
        bool r500746 = r500742 <= r500745;
        double r500747 = !r500746;
        bool r500748 = r500744 || r500747;
        double r500749 = x;
        double r500750 = r500740 / r500738;
        double r500751 = r500736 / r500738;
        double r500752 = r500750 - r500751;
        double r500753 = r500737 / r500752;
        double r500754 = r500749 + r500753;
        double r500755 = r500749 + r500742;
        double r500756 = r500748 ? r500754 : r500755;
        return r500756;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original10.2
Target0.6
Herbie0.3
\[\begin{array}{l} \mathbf{if}\;t \lt -1.0682974490174067 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;t \lt 3.9110949887586375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (* (- y z) t) (- a z)) < -inf.0 or 1.2683856510205498e+298 < (/ (* (- y z) t) (- a z))

    1. Initial program 63.4

      \[x + \frac{\left(y - z\right) \cdot t}{a - z}\]
    2. Using strategy rm

    3. Applied associate-/l*0.3

      \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t}}}\]
    4. Using strategy rm

    5. Applied div-sub0.3

      \[\leadsto x + \frac{y - z}{\color{blue}{\frac{a}{t} - \frac{z}{t}}}\]

    if -inf.0 < (/ (* (- y z) t) (- a z)) < 1.2683856510205498e+298

    1. Initial program 0.3

      \[x + \frac{\left(y - z\right) \cdot t}{a - z}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} = -\infty \lor \neg \left(\frac{\left(y - z\right) \cdot t}{a - z} \le 1.2683856510205498 \cdot 10^{298}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t} - \frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020003 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (if (< t -1.0682974490174067e-39) (+ x (* (/ (- y z) (- a z)) t)) (if (< t 3.9110949887586375e-141) (+ x (/ (* (- y z) t) (- a z))) (+ x (* (/ (- y z) (- a z)) t))))

  (+ x (/ (* (- y z) t) (- a z))))